If you want to build a custom circuit for the arduino to connect to you can purchase a prototype shield or take some proto board and build your circuit onto the proto board. On the proto shield there are pin holes to mount pin headers and then can mount the proto board to your arduino.
Much safer and then you can easily change proto boards for different projects. If the circuit is somewhat larger. you can create a larger proto board and use a ribbon cable to connect the header pins from your proto board to your Arduino.